Rectangular pipe-jacking tunnel longitudinal torsional rigidity effective rate calculation method and system and storage medium

Abstract

The invention discloses a method and system for calculating the longitudinal torsional rigidity effective rate of a rectangular pipe-jacking tunnel under combined acting force and a storage medium. The method comprises the following steps that S1, the bending-pressing-twisting combined acting force on a calculation unit of the rectangular pipe-jacking tunnel is obtained according to the stress condition of the rectangular pipe-jacking tunnel; s2, the stress state of the pipe jacking lining structure is judged according to the relation between the bending moment and the axial force, and the stress state of the structure is divided into two different conditions according to the position of a neutral axis; s3, for different stress states, according to deformation coordination conditions and mechanical equilibrium conditions, calculating the distance between a neutral axle on the section and the center of the section; s4, according to the torque balance condition and further according to the two different conditions, the position of the torsion center and the anti-friction torque generated by the concrete in the pressed area are calculated; and S5, calculating a joint torsion angle and equivalent torsional rigidity, and further calculating the effective rate of the torsional rigidity. The longitudinal torsional rigidity effective rate of the rectangular pipe-jacking tunnel under the bending, pressing and twisting combined acting force can be rapidly and accurately obtained, and a basis is provided for structural safety analysis of the rectangular pipe-jacking tunnel.

Description

Technical Field

[0001] The present invention belongs to the technical field of underground engineering, and particularly relates to a method, a system and a storage medium for calculating the longitudinal torsional stiffness efficiency of a rectangular pipe-jacking tunnel. Background Art

[0002] Under external forces, a rectangular pipe-jacking tunnel is prone to longitudinal non-uniform deformation, which may further lead to diseases such as non-uniform settlement, joint opening, water leakage, etc. Compared with a rectangular shield tunnel, a rectangular pipe-jacking tunnel has fewer longitudinal bolts. Especially for the existing large-section rectangular pipe-jacking tunnels, the number of its longitudinal bolts is much smaller than that of a rectangular shield tunnel of the same scale. At the same time, there is an additional force-bearing component, i.e., a steel sleeve ring, in the longitudinal joint of a rectangular pipe-jacking tunnel compared with a rectangular shield tunnel. The steel sleeve ring has little influence on its flexural performance but has a greater influence on its shear performance. Therefore, under the same external load, compared with a rectangular shield tunnel, the joint opening of a rectangular pipe-jacking tunnel is larger, and it is more likely to produce longitudinal non-uniform torsional deformation. Moreover, in torsional calculation, the influence of the steel sleeve ring should be additionally considered. Therefore, it is necessary to study the longitudinal torsional stiffness efficiency of a rectangular pipe-jacking tunnel.

[0003] During the construction and operation of a rectangular pipe-jacking tunnel, it often faces various non-uniform loads such as excavation of surrounding soil, ground eccentric load, ground fissure, etc., which may lead to non-uniform torsional action. Excessive non-uniform torsion will cause large stresses and deformations in the pipe segments, bolts and steel sleeve rings of the pipe-jacking, and result in circumferential joint dislocation and track inclination, seriously affecting the tunnel safety. At present, the engineering community has insufficient understanding and attention to the tunnel torsion problem. The main research focuses on the flexural and shear performance of tunnel joints, and there is little research on the torsional performance of tunnels, especially the torsional performance of rectangular pipe-jacking tunnels. For a rectangular pipe-jacking tunnel, although the tunnel torsional performance is an important factor to ensure the structural safety of the rectangular tunnel, there is currently no research on the longitudinal torsional performance of rectangular pipe-jacking tunnels. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a method, a system and a storage medium for calculating the longitudinal torsional stiffness efficiency of a rectangular pipe-jacking tunnel to solve the deficiencies in the prior art.

[0005] To achieve the above purpose, the present invention is implemented by the following technical solutions:

[0006] On the one hand, a method for calculating the longitudinal torsional stiffness efficiency of a rectangular pipe-jacking tunnel is provided. The rectangular pipe-jacking tunnel is composed of lining segments, steel sleeve rings and circumferential joints. Among them, the method includes the following steps:

[0007] S1. Take two adjacent half-segments and the circumferential joint of the rectangular pipe-jacking tunnel as a calculation unit, and obtain the combined bending-compression-torsion force on a calculation unit according to the stress condition of the rectangular pipe-jacking tunnel;

[0008] S2. According to the relationship between the bending moment M and the axial force N, judge the stress state of the tunnel structure, and divide the stress state of the tunnel structure into two different cases according to the position of the neutral axis: when the neutral axis is within the cross-section, the circumferential joint opens, and the concrete at the circumferential joint is compressed at one end and tensioned at the other end; when the neutral axis is outside the cross-section, the circumferential joint closes, and the concrete at the circumferential joint is all compressed;

[0009] S3. For different stress states, calculate the distance c from the neutral axis to the center of the cross-section on the cross-section according to the deformation compatibility condition and the mechanical equilibrium condition;

[0010] S4. According to the torque balance condition, further calculate the position a of the torsion center and the anti-friction torque T generated by the compressed concrete in the compression zone respectively for these two different cases c ;

[0011] S5. Calculate the joint torsion angle and the equivalent torsional stiffness (GI) eq , and further calculate the effective rate ξ of the torsional stiffness.

[0012] As the method for calculating the effective rate of the longitudinal torsional stiffness of the rectangular pipe-jacking tunnel, wherein, the determination criterion for the bending moment and the axial force is:

[0013] N lim = M * A s * h / I s ;

[0014] Where N lim is the boundary axial force that closes the circumferential joint under the bending moment M, A s is the cross-sectional area of the segment, h is half of the segment height, I s is the moment of inertia of the segment cross-section. For a rectangular pipe-jacking tunnel, I s = 4h 2 t(b + h / 3), b is half of the segment width, and t is the segment thickness;

[0015] When N < N lim , the neutral axis is within the cross-section, the circumferential joint opens, and the concrete at the circumferential joint is compressed at one end and tensioned at the other end; when N ≥ N lim , the neutral axis is outside the cross-section, the circumferential joint closes, and the concrete at the circumferential joint is all compressed.

[0016] As the method for calculating the effective rate of the longitudinal torsional stiffness of the rectangular pipe-jacking tunnel, wherein, when the neutral axis is within the cross-section, the deformation compatibility condition is:

[0017]

[0018] In the formula, ε c and ε tare the compressive strain and tensile strain at the top and bottom of the segment, respectively, l s is the segment width, δ j is the width of the segment opening, α is the rotation angle within the annular gap, and c is the distance between the neutral axis and the center of the section;

[0019] The mechanical equilibrium condition is:

[0020]

[0021] In the formula, E s is the elastic modulus of concrete, k rh is the bolt line stiffness, E b is the elastic modulus of the bolt.

[0022] For example, in the effective calculation method of the longitudinal torsional stiffness of a rectangular pipe-jacking tunnel, when the neutral axis is outside the cross section, the deformation coordination condition is:

[0023]

[0024] The mechanical equilibrium condition is:

[0025]

[0026] In the formula, ε c1 and ε c2 are the maximum and minimum compressive strains of concrete at the joints, respectively.

[0027] For example, the effective calculation method of the longitudinal torsional stiffness of a rectangular jacking tunnel is as follows: when the neutral axis is within the cross section, the distance a between the torsion center and the cross section center can be obtained by combining the following formulas:

[0028] F bx +F cx =0

[0029]

[0030] T=T c +T b

[0031]

[0032] In the formula, F bx is the component of the bolt shear force in the x direction, F cx is the component of concrete shear force in the x direction, is the joint torsion angle, T c is the friction torque generated by the concrete compressive stress, T b is the torque generated by the bolt, K t is the average shear stiffness of the bolts in the annular joint, Kg is the shear stiffness of the steel collar.

[0033] For example, the effective calculation method of the longitudinal torsional stiffness of a rectangular pipe-jacking tunnel is as follows: when the neutral axis is outside the cross section, the distance a between the torsion center and the cross section center can be obtained by combining the following formulas:

[0034] F bx +F cx =0

[0035]

[0036] T=T c +T b

[0037]

[0038] In the formula, σ c1 and σ c2 are the maximum and minimum compressive stresses of concrete at the joints, respectively.

[0039] As described in the calculation method of the effective longitudinal torsional stiffness of a rectangular pipe-jacking tunnel, when the neutral axis is within the cross section, the friction torque T generated by the concrete in the compression zone is c satisfy:

[0040]

[0041] As described in the calculation method of the effective longitudinal torsional stiffness of a rectangular pipe-jacking tunnel, when the neutral axis is outside the cross section, the friction torque T generated by the concrete in the compression zone is c satisfy:

[0042]

[0043] As described above, the effective calculation method of the longitudinal torsional stiffness of a rectangular pipe-jacking tunnel is as follows: c When , the torsional stiffness efficiency ξ satisfies:

[0044]

[0045] When T<T c When , the torsional stiffness effective rate ξ is 1.

[0046] On the other hand, the present invention provides a system for calculating the effective rate of longitudinal torsional stiffness of a rectangular pipe jacking tunnel, which comprises a computer-readable storage medium and a processor, wherein the computer-readable storage medium is used to store executable instructions, and the processor is used to read the executable instructions stored in the computer-readable storage medium to execute any one of the methods for calculating the effective rate of longitudinal torsional stiffness of a rectangular pipe jacking tunnel.

[0047] In another aspect, the present invention provides a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, it implements the method for calculating the longitudinal torsional stiffness efficiency of any rectangular pipe-jacking tunnel.

[0048] The beneficial effects of the technical solution of the present invention are as follows:

[0049] 1. The method for calculating the longitudinal torsional stiffness efficiency of the rectangular pipe-jacking tunnel of the present invention considers the combined bending-compression-torsion forces M-N-T acting on a calculation unit of the rectangular pipe-jacking tunnel, judges the deformation state of the circumferential joints of the rectangular pipe-jacking ring according to its specific stress conditions, and calculates the two states of circumferential joint opening and circumferential joint closing respectively. According to the deformation coordination condition and the mechanical equilibrium condition, the distance c from the neutral axis of the cross-section to the center of the cross-section is calculated, and further the position a of the torsion center and the anti-friction torque T generated by the concrete in the compression zone are calculated according to the torque balance condition. c Finally, the longitudinal torsional stiffness efficiency ξ of the rectangular pipe-jacking tunnel is obtained; the method of the present invention realizes the calculation of the longitudinal torsional stiffness efficiency of the rectangular pipe-jacking tunnel, can better characterize the anti-torsion performance of the rectangular pipe-jacking tunnel, and provides a basis for the anti-torsion characteristics of the rectangular pipe-jacking tunnel during construction and operation.

[0050] 2. The present invention provides a method for judging the stress state of a rectangular pipe-jacking tunnel. According to the relationship between the bending moment M and the axial force N, the opening and closing states of the circumferential joints of the rectangular pipe-jacking tunnel are judged. By the relationship between the external torsional load T and the anti-friction torque T generated by the concrete in the compression zone. c The relationship judges whether the circumferential joints of the rectangular pipe-jacking tunnel have been twisted, which is convenient for the project to quickly judge the stress and deformation characteristics of the rectangular pipe-jacking tunnel.

[0051] All in all, the present invention can quickly and accurately obtain the longitudinal torsional stiffness efficiency of the rectangular pipe-jacking tunnel under the combined bending-compression-torsion forces, providing a basis for the structural safety analysis of the rectangular pipe-jacking tunnel. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] To further illustrate the above objects, structural features and effects of the present invention, the present invention will be described in detail below with reference to the accompanying drawings.

[0053] Figure 1 It is a schematic diagram of the method for calculating the longitudinal torsional stiffness efficiency of the rectangular pipe-jacking tunnel according to a preferred embodiment of the present invention;

[0054] Figure 2 It is a flow chart of the method for calculating the longitudinal torsional stiffness efficiency of the rectangular pipe-jacking tunnel according to a preferred embodiment of the present invention;

[0055] Figure 3a It is a schematic diagram of the longitudinal anti-torsion of the tunnel according to a preferred embodiment of the present invention;

[0056] Figure 3b Schematic diagram of the torsion calculation unit in the preferred embodiment of the present invention;

[0057] Figure 3c Simplified schematic diagram of bolt deformation in the preferred embodiment of the present invention;

[0058] Figure 4 Distribution diagram of the torsional force on the joint seam in the preferred embodiment of the present invention;

[0059] Figure 5 Distribution diagram of stress and deformation in the circumferential seam under the combined action of bending, compression and torsion in the preferred embodiment of the present invention (neutral axis is within the cross-section);

[0060] Figure 6 Distribution diagram of stress and deformation in the circumferential seam under the combined action of bending, compression and torsion in the preferred embodiment of the present invention (neutral axis is outside the cross-section);

[0061] Figure 7 Schematic diagram of the cross-sectional dimensions of the rectangular pipe jacking in the preferred embodiment of the present invention;

[0062] Figure 8 Result diagram of the change of the effective rate of the longitudinal torsional stiffness of the rectangular pipe jacking with the axial force in the preferred embodiment of the present invention;

[0063] Figure 9 Result diagram of the change of the effective rate of the longitudinal torsional stiffness of the rectangular pipe jacking with the bending moment in the preferred embodiment of the present invention. Detailed implementation manners

[0064] The terms "invention" and "the present invention" as used in this specification are intended to broadly refer to all the subject matters of this specification and any of the following patent claims. Statements containing these terms should not be construed as limiting the subject matter described herein or the meaning or scope of any of the following patent claims. In addition, this specification does not attempt to describe or limit the subject matter covered by any specific component, paragraph, statement or claim of this application. The subject matter should be understood with reference to the entire specification, all the drawings and any of the following claims. The present invention may have other embodiments and may be practiced or implemented in other ways. Moreover, it should be understood that the wording and terms used herein are for illustrative purposes and should not be considered limiting.

[0065] Details of the present invention will now be discussed with reference to the drawings of the present invention, which are provided by way of example only. In the drawings, like features or components may be labeled with the same reference numerals.

[0066] As used herein, the terms "comprising", "having", "including" and their variants are intended to cover the listed items and their equivalents and additional items. Although directions such as above, below, upward, downward, backward, bottom, top, front, back, etc. may be referred to in the description of the drawings for convenience with reference to the drawings, these directions are not intended to be literally accepted or limit the present invention in any way. In addition, terms such as "first", "second", "third", etc. are used herein for illustrative purposes and are not intended to indicate or imply importance or significance.

[0067] The main object of the present invention is to analyze the longitudinal torsional stiffness efficiency of a rectangular pipe-jacked tunnel under the combined action of bending, compression and torsion, and to provide a basis for the analysis of the torsional performance of rectangular pipe-jacked tunnels in practical engineering.

[0068] See Figure 1 、 Figure 2 As shown in the preferred embodiment, the method for calculating the bending stiffness efficiency of the rectangular pipe-jacked tunnel of the present invention mainly includes:

[0069] S1. Take two adjacent half-segment rings and the ring joint of the rectangular pipe-jacked tunnel as a calculation unit, and obtain the combined bending-compression-torsion force M-N-T on a calculation unit according to the stress condition or monitoring result of the rectangular pipe-jacked tunnel. The structural deformation mode and stress distribution of the rectangular pipe-jacked tunnel are respectively as shown in Figure 3a 、 Figure 3b 、 Figure 3c and Figure 4 shown.

[0070] S2. According to the relationship between the bending moment M and the axial force N, judge the stress state of the tunnel structure, and accordingly divide the stress state of the tunnel structure into two different situations. When the neutral axis is within the cross-section, the ring joint opens, and the concrete at one end of the ring joint is compressed and the other end is tensioned; when the neutral axis is outside the cross-section, the ring joint closes, and the concrete at the ring joint is all compressed. The stress and deformation distribution diagrams of the ring joint when the neutral axis is within the cross-section are as shown in Figure 5 shown, and the stress and deformation distribution diagrams of the ring joint when the neutral axis is outside the cross-section are as shown in Figure 6 shown.

[0071] S3. According to the different situations of the tunnel stress state, list the deformation coordination conditions and mechanical equilibrium conditions in this situation, and calculate the distance c from the neutral axis of the cross-section to the center of the cross-section.

[0072] S4. According to the torque balance condition, further calculate the position a of the torsion center and the anti-friction torque T generated by the concrete in the compression zone respectively according to these two different situations c .

[0073] S5. Calculate the joint torsion angle and the equivalent torsional stiffness (GI) eq, and further calculate the effective rate ξ of the torsional stiffness.

[0074] Specifically, the bending moment M, axial force N, and torque T on the calculation unit obtained in S1, together with the cross-section design parameters and joint design parameters of the rectangular pipe-jacking tunnel, are all the initial conditions of this calculation method.

[0075] Specifically, in S2, first calculate the boundary axial force N that closes the circumferential joint under the bending moment M lim :

[0076] N lim = M * A s * h / I s ;

[0077] In the formula, N lim is the boundary axial force that closes the circumferential joint under the bending moment M, A s is the cross-sectional area of the segment, h is half of the segment height, I s is the moment of inertia of the segment cross-section. For a rectangular pipe-jacking tunnel, I s = 4h 2 t(b + h / 3), where b is half of the segment width and t is the segment thickness.

[0078] Judge the stress state of the tunnel according to the relationship between N and N lim . When N < N lim , the neutral axis is within the cross-section, the circumferential joint opens, and the concrete at the circumferential joint is compressed at one end and tensioned at the other end; when N ≥ N lim , the neutral axis is outside the cross-section, the circumferential joint closes, and the concrete at the circumferential joint is all compressed.

[0079] Specifically, in S3 - S4, according to the different stress states of the tunnel, list different deformation coordination conditions and mechanical equilibrium conditions, etc., to calculate the position c of the neutral axis, the position a of the torsional center, and the anti-friction torque T generated by the concrete in the compression zone c .

[0080] When the neutral axis is within the cross-section, the deformation coordination conditions and mechanical equilibrium conditions in S3:

[0081]

[0082] In the formula, ε c and ε t are the compressive strain and tensile strain at the top and bottom of the segment respectively, l s is the segment ring width, δ j is the width of the segment opening, α is the rotation angle within the circumferential joint range, c is the distance between the neutral axis and the cross-section center, E s is the elastic modulus of concrete, k rh is the bolt line stiffness, and E b is the elastic modulus of the bolt.

[0083] By solving the equations simultaneously, the position c of the neutral axis satisfies:

[0084]

[0085] where K j is the total stiffness of the bolts.

[0086] By iterative solution, the position c of the neutral axis can be obtained.

[0087] Furthermore, the longitudinal flexural stiffness efficiency η, the circumferential joint opening angle α, and the maximum compressive stress σ of the concrete at the joint of the rectangular pipe jacking can be calculated by the following formula: c :

[0088]

[0089] Similarly, when the neutral axis is within the cross-section, in S4, the distance a from the torsional center to the center of the cross-section can be obtained by solving the following equations simultaneously:

[0090]

[0091] where F bx is the component of the bolt shear force in the x-direction, F cx is the component of the concrete shear force in the x-direction, is the joint torsional angle, T c is the frictional torque generated by the concrete compressive stress, T b is the torque generated by the bolts, K t is the average shear line stiffness of the circumferential joint, K g is the shear line stiffness of the steel sleeve ring. K t can be calculated by the following formula:

[0092]

[0093] where n is the total number of bolts on the cross-section, K b is the equivalent shear stiffness, K b = κ b G b A b / (λl b ), κ b is the shear correction factor of the bolt, A b is the cross-sectional area of the bolt, G b is the shear stiffness modulus of the bolt, l b is the bolt length, and λ is the effective shear length coefficient of the bolt.

[0094] K g can be calculated by the following formula:

[0095]

[0096] Where G g is the shear stiffness modulus of the steel sleeve ring, t g is the thickness of the steel sleeve ring, l g is the ring width of the steel sleeve ring, λ g is the effective shear length coefficient of the steel sleeve ring.

[0097] By solving the equations simultaneously, the position a of the torsional center of the cross-section can be obtained as satisfying:

[0098]

[0099] Furthermore, the anti-friction torque T generated by the concrete in the compression zone can be calculated as: c :

[0100]

[0101] When the neutral axis is within the cross-section, the deformation coordination condition and mechanical equilibrium condition in S3 are:

[0102]

[0103] Where ε c1 and ε c2 are respectively the maximum compressive strain and minimum compressive strain of the concrete at the joint. σ c1 and σ c2 are respectively the maximum compressive stress and minimum compressive stress of the concrete at the joint.

[0104] By solving the equations simultaneously, the position c of the neutral axis can be obtained as satisfying:

[0105]

[0106] Furthermore, the circumferential seam opening angle α of the rectangular pipe jacking, the maximum compressive strain ε c1 and minimum compressive strain ε c2 of the concrete at the joint, as well as the maximum compressive stress σ c1 and minimum compressive stress σ c2 can be calculated by the following formula:

[0107]

[0108] Similarly, when the neutral axis is outside the cross-section, in S4, the distance a from the torsional center to the center of the cross-section can be obtained by solving the following equations simultaneously:

[0109]

[0110] By solving the equations simultaneously, the position a of the torsional center of the cross-section can be obtained as satisfying:

[0111]

[0112] Furthermore, the anti-friction torque T generated by the concrete in the compression zone can be calculated. c :

[0113]

[0114] Specifically, in S5, when the external torsional load T > T c , the effective rate ξ of the torsional stiffness can be calculated by the following formula:

[0115]

[0116] where θ s is the relative torsional angle of the segment, (GI) eq is the equivalent torsional stiffness, and (GI) s is the torsional stiffness of the tunnel segment.

[0117] In S5, when T ≤ T c , the effective rate ξ of the torsional stiffness is 1.

[0118] To further explain the method of the present invention, in the embodiments of the present invention, a certain rectangular pipe-jacking tunnel is taken as an analysis object for specific analysis. The dimensions of the analysis object are as Figure 7 shown. The segments of the rectangular pipe-jacking tunnel adopt C50 concrete, and the elastic modulus E s of the concrete is taken as 34500 MPa, the length l b of the bolt is taken as 0.6 m, the diameter d of the bolt is taken as 30 mm, the elastic modulus E b of the bolt is taken as 200 GPa, the shear modulus G b of the bolt is taken as 80 GPa, the effective shear length λ b of the bolt is taken as 0.33, the width l g of the steel sleeve ring is taken as 500 mm, the thickness t g of the steel sleeve ring is taken as 10 mm, the shear modulus G g of the steel sleeve ring is taken as 80 GPa, the effective shear length λ g of the steel sleeve ring is taken as 1, the friction coefficient f c between the concretes is taken as 0.2, and the segment ring width l s is taken as 1.5 m. Figure 8 In, the torsional moment T is taken as 2 MN·m, the bending moment M is taken as 2 MN·m, and the axial force N varies from 0 to 3.2 MN, that is, the compression-torsion ratio varies from 0 to 1.6. Figure 9 In, the torsional moment T is taken as 2 MN·m, the axial force N is taken as 1 MN, and the bending moment M varies from 0 to 18 MN·m, that is, the bending-torsion ratio varies from 0 to 9.

[0119] Figure 8 shows the relationship between the effective rate of the equivalent torsional stiffness and the compression-torsion ratio. From Figure 8It can be seen that in the initial state, the effective rate of the equivalent torsional stiffness is about 0.62, and then it increases with the increase of the axial pressure; when the compression-torsion ratio N / T increases to 1.37m -1 , the effective rate of the equivalent torsional stiffness is 1, and the circumferential joint no longer undergoes torsion. Figure 9 The relationship between the effective rate of the equivalent torsional stiffness and the bending-torsion ratio is shown. From Figure 9 it can be seen that as the bending-torsion ratio increases from 0 to 9, the effective rate of the equivalent torsional stiffness first decreases from 0.684 to 0.672, and then gradually increases to 1. When the bending-torsion ratio M / T exceeds 7.6, the effective rate of the equivalent torsional stiffness is 1, and there is no torsion in the circumferential joint. Figure 8 And Figure 9 The analysis results show that the method of the present invention can effectively analyze the effective rate of the longitudinal torsional stiffness of a rectangular pipe-jacking tunnel under the combined action of bending, compression and torsion.

[0120] The present invention also provides a system for calculating the effective rate of the longitudinal torsional stiffness of a rectangular pipe-jacking tunnel, including a computer-readable storage medium and a processor. The computer-readable storage medium is used to store executable instructions, and the processor is used to read the executable instructions stored in the computer-readable storage medium and execute the method for calculating the effective rate of the longitudinal torsional stiffness of a rectangular pipe-jacking tunnel in the above embodiments.

[0121] The present invention also provides a computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, it implements the method for calculating the effective rate of the longitudinal torsional stiffness of a rectangular pipe-jacking tunnel as in the above embodiments.

[0122] The method for calculating the effective rate of the longitudinal torsional stiffness of a rectangular pipe-jacking in the present invention considers the combined action of bending-compression-torsion M-N-T on a calculation unit of a rectangular pipe-jacking tunnel, judges the deformation state of the circumferential joint of the rectangular pipe-jacking according to its specific stress situation, and calculates the two states of the circumferential joint opening and the circumferential joint closing respectively. According to the deformation coordination condition and the mechanical equilibrium condition, the distance c from the neutral axis of the cross-section to the center of the cross-section is calculated, and further the position a of the torsion center and the anti-friction torque T generated by the concrete in the compression zone are calculated according to the torque balance condition c , and finally the effective rate ξ of the longitudinal torsional stiffness of the rectangular pipe-jacking tunnel is obtained. The method of the present invention realizes the calculation of the effective rate of the longitudinal torsional stiffness of a rectangular pipe-jacking tunnel, can better characterize the anti-torsion performance of a rectangular pipe-jacking tunnel, and provides a basis for the anti-torsion characteristics of a rectangular pipe-jacking tunnel in construction and operation.

[0123] In the embodiments of the present invention, for the above S2 - S5, a program is independently written using Matlab software. When the method of the present invention is actually applied, only the corresponding parameters need to be obtained, including the cross - section design parameters of the rectangular pipe - jacking tunnel, the joint design parameters, and the bending moment, pressure, and torque acting on the calculation unit. By running the corresponding code, the longitudinal torsional stiffness efficiency of the calculation unit under the current working condition can be quickly obtained without relying on any simulation platform. The method is simple and efficient and has strong versatility. The present invention can be applied to the design and operation of rectangular pipe - jacking tunnels, and the obtained results can assist engineers in quickly judging the torsional performance of rectangular pipe - jacking tunnels.

[0124] The above are only the preferred embodiments of the present invention, and thus do not limit the implementation manners and protection scope of the present invention. For those skilled in the art, it should be realized that all the equivalent replacements and obvious changes made by using the description and illustrations of the present invention should be included in the protection scope of the present invention.

Claims

1. A calculation method for the effective longitudinal torsional stiffness efficiency of a rectangular pipe-jacking tunnel. The rectangular pipe-jacking tunnel is composed of lining segments, steel collar rings, and circumferential joints, and is characterized in that The following steps are involved: S1, taking two adjacent half-segment rings and annular seams of a rectangular jacking tunnel as a calculation unit, and obtaining the bending-compression-torsion combined force on one calculation unit according to the stress condition of the rectangular jacking tunnel; S2. According to the relationship between the bending moment M and the axial force N, the stress state of the tunnel structure is determined, and the stress state of the tunnel structure is divided into two different situations according to the position of the neutral axis: when the neutral axis is inside the cross section, the annular joint is open, and one end of the concrete at the annular joint is under compression and the other end is under tension; when the neutral axis is outside the cross section, the annular joint is closed, and the concrete at the annular joint is under compression; S3. According to the different stress states, the distance c between the neutral axis on the cross section and the cross section center is calculated according to the deformation coordination condition and the mechanical equilibrium condition; S4. According to the torque balance condition, further calculate the position a of the torsion center and the anti-friction torque T generated by the concrete in the compression zone respectively according to these two different situations c ; S5. Calculate the joint torsion angle and the equivalent torsional stiffness (GI) eq , and further calculate the effective rate ξ of the torsional stiffness 2. The method for calculating the effective rate of longitudinal torsional stiffness of a rectangular pipe-jacking tunnel according to claim 1, wherein The criteria for determining the bending moment and axial force are: N lim = M * A s * h / I s ; Where N lim is the critical axial force that closes the circumferential joint under the bending moment M, A s is the cross-sectional area of the segment, h is half of the segment height, I s is the moment of inertia of the segment cross-section. For a rectangular pipe-jacking tunnel, I s = 4h 2 t(b + h / 3), where b is half of the segment width and t is the segment thickness; When N < N lim , the neutral axis is within the cross-section, the circumferential joint opens, and the concrete at the circumferential joint is compressed at one end and tensioned at the other end; when N ≥ N lim , the neutral axis is outside the cross-section, the circumferential joint closes, and the concrete at the circumferential joint is all compressed.

3. The method for calculating the effective rate of longitudinal torsional stiffness of a rectangular pipe-jacking tunnel according to claim 2, wherein When the neutral axis is within the cross section, the deformation coordination condition is: where ε c and ε t are the compressive strain and tensile strain at the top and bottom of the segment respectively, l s is the width of the segment ring, δ j is the width of the segment opening, α is the rotation angle within the circumferential joint, and c is the distance between the neutral axis and the center of the cross-section; The mechanical equilibrium condition is: where, E s is the elastic modulus of concrete, k rh is the wire stiffness of the bolt, E b is the elastic modulus of the bolt.

4. The calculation method for the effective rate of longitudinal torsional stiffness of a rectangular pipe-jacking tunnel according to claim 2, characterized in that, When the neutral axis is outside the cross section, the deformation coordination condition is: The mechanical equilibrium condition is: where ε c1 and ε c2 are the maximum compressive strain and the minimum compressive strain of the concrete at the joint, respectively.

5. The method for calculating the effective rate of the longitudinal torsion resistance stiffness of the rectangular pipe-jacking tunnel according to claim 3, characterized in that When the neutral axis is within the cross section, the distance a between the torsion center and the cross section center can be obtained by combining the following formulas: F bx +F cx =0 T = T c + T b Where, F bx is the component of the bolt shear force in the x direction, F cx is the component of the concrete shear force in the x direction, is the joint torsional angle, T c is the frictional torque generated by the concrete compressive stress, T b is the torque generated by the bolt, K t is the average shear line stiffness of the bolts in the circumferential joint, K g is the shear line stiffness of the steel sleeve ring.

6. The method for calculating the effective rate of the longitudinal torsion resistance stiffness of a rectangular pipe-jacking tunnel according to claim 4, characterized in that When the neutral axis is outside the cross section, the distance a between the torsion center and the cross section center can be obtained by combining the following formulas: F bx +F cx =0 T = T c + T b In the formula, σ c1 and σ c2 are respectively the maximum compressive stress and the minimum compressive stress of the concrete at the joint.

7. The method for calculating the effective rate of the longitudinal torsional stiffness of a rectangular pipe-jacking tunnel according to claim 5, wherein When the neutral axis is within the cross-section, the anti-friction torque T generated by the concrete in the compression zone c satisfies:

8. The calculation method for the effective longitudinal torsion resistance stiffness of a rectangular pipe-jacking tunnel according to claim 6, characterized in that When the neutral axis is outside the cross-section, the anti-friction torque T generated by the concrete in the compression zone c satisfies:

9. The method for calculating the effective rate of the longitudinal torsion resistance stiffness of the rectangular pipe-jacking tunnel according to claim 7 or 8, wherein When the external torsional load T > T c , the efficiency ξ of the torsional stiffness satisfies: When T < T c the efficiency ξ of the torsional stiffness is 1.

10. A calculation system for the effective rate of the longitudinal torsional stiffness of a rectangular pipe-jacking tunnel, characterized in that, It comprises a computer-readable storage medium and a processor, wherein the computer-readable storage medium is used to store executable instructions, and the processor is used to read the executable instructions stored in the computer-readable storage medium to execute the method for calculating the effective rate of longitudinal torsional stiffness of a rectangular jacking tunnel as described in any one of claims 1 to 9.

11. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, the method for calculating the effective longitudinal torsional stiffness of a rectangular pipe-jacking tunnel as described in any one of claims 1 to 9 is implemented.

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